How can I show a multipage post as a single, wrapped post?

Since it looks like there’s no existing way to do this, here’s my solution. It just splits the content on the pagebreak tag, parses the HTML and wraps each page in a div:

function get_paginated_post($post) {
    $pagebreak = '<!--nextpage-->';
    $raw_post = $post->post_content;
    $pages = explode($pagebreak, $raw_post);
    $html="";
    foreach ($pages as $p=>$page) {
        $html .= '<div class="page-' . ($p+1) . '">' . apply_filters('the_content', $page) . '</div>';
    }
    return $html;
}

Not beautiful, but does the job.